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Questions tagged [two-stage-least-squares]

Two-stage least squares (2SLS) is a structural equation modeling technique that is used when the IV is correlated with the DV's errors.

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2SLS: does it just rescale the instrument variable?

I am investigating using instrument variables to correct for some known sources of measurement error in my data (measures that reflect mistakes/inconsistencies that we think directly affect our main ...
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Does an instrumental variable require independence between the instrument and treatment?

An instrumental variable Z is a legitimate instrument for T (the treatment) if the following hold: Z has a causal effect on Y that is fully mediated by T (i.e. no direct effect from Z to Y, and the ...
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Do first and second stage regressions combined with fixed effects have to follow the same model?

I suspect reverse causality between Y and X1, therefore I'm applying an instrumental variable approach to panel data. My main regression consists of country- and year-fixed effects. Do I have to also ...
TFT's user avatar
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Instrumental variable with measurement error

I have a question related to measurement error bias and the use of instrumental variables. Assume I have a continuous outcome variable $Y$ which is observed with no error and an endogenous (continuous)...
Panagiotis's user avatar
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Weak instrument but 2nd stage significant

My IV's 1st stage F-stat is 4.7 (considered weak by the rule of thumb). The 2nd-stage regression coefficient is significant. I wonder what is the best way to interpret such observations.
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Partial derivative of interaction term with endogenous variable

I am trying to estimate the price elasticity based on a 2sls regression. The price in logarithmic form is treated as an endogenous variable. The price appears in an interaction term with income $\...
octopus161's user avatar
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What is a 2-stage estimator?

I thought I would quickly find the answer to this, and maybe my capabilities of using the sites search function are very poor, but I didn't find an answer to the definition of what a 2-stage estimator ...
Lynchian's user avatar
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warning: variance matrix is nonsymmetric or highly singular [closed]

I get the above warning when running a 2SLS regression in Stata with robust standard errors. Specifically, I get this for the first stage, where in addition the first stage has no F-statistic, p-value,...
john_hawthorne's user avatar
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Temporal Order of Control Variables in 2SLS

I am analyzing pooled cross-sectional data with the instrumental variable being educational policy, the independent variable as high school graduation, and the dependent variable as subjective class ...
Nobody Nobody's user avatar
2 votes
1 answer
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Estimating Complier Average Causal Effect (CACE) in a Field Experiment with One-Sided Noncompliance

I am working on a referee report for a field experiment focused on the employment process. The experiment investigates if including a video in job applications can reduce employment disadvantages for ...
john_hawthorne's user avatar
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2sls with interaction terms

I am running 2sls. Dependent variable - y Independent variable - x Instrumental variables - z1, z2, z3, z4 Interaction terms - xz1, xz2, xz3, xz4 Control variables Thus, the first stage of 2sls: x ...
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How to evaluate the effect of each group in dummy D to endogenous variable X in 2SLS regression?

I have a question in terms of evaluating the effect of a dummy $D$ to endogenous variable $X$ in two-stage least squares (2SLS) regression. Suppose I have dependent variable $Y$, endogenous variable $...
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Discrepancy in 2SLS Estimation Results

I've been exploring the 2SLS (Two-Stage Least Squares) estimation method to analyze a model involving endogeneity and instrumental variables. To better understand the process, I performed manual ...
lasagna's user avatar
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The magnitude of an two-stages least squares coefficient is always larger than the ordinary least squares coefficient?

I have a hard time wrapping my head around this. I know that in case of measurement errors, the OLS estimate is biased downwards zero. Omitted variables can bias the explanatory variable of interest ...
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IVs: would this rainfall specification cut it?

I need feedback to check whether rainfall is an appropriate instrumental variable. Before you boo me out, hear what I have to say. There are two countries: A and B. A and B are 2000 miles apart. My ...
YouLocalRUser's user avatar
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2SLS with endogenous variable $X_1$ and interaction terms $X_1 \times X_2$, $X_2$ exogenous

I would like clarification on the correct way to set up the first-stage regression(s) for a hypothetical 2SLS regression. Say we have the following formula: \begin{align} y = x_1 + x_2 + x_1 \...
Pancho_Squancho's user avatar
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Instrumental variable identifiability in a linear setting in the presence of unobserved confounders

Long story short, I'm seeing in the literature that linear instrumental variables models are identifiable, even in the presence of unobserved confounders. The unobserved confounding aspect befuddles ...
mortonjt's user avatar
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When is an instrument too strong in the first stage?

Instrumental variable regression is estimated with ivreg in R. ivreg provides diagnostics with the ...
Marco's user avatar
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Can a variable be an instrument in the first stage and an exogenous covariate in the second stage of an 2SLS regression?

I have two equations of the form: $y = X\beta + Z\gamma + r\alpha +\epsilon_1$ (1) $r = Z\delta +\epsilon_2$ (2) The basic intuition here is $y$ is total cost data, $X$ is a matrix of variables ...
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Can I have an interaction-term between the predicted endogenous variable and other exogenous variables in the second stage Modell of a 2SLS?

I have a question regarding 2SLS and interaction-terms between the predicted endogenous variable and a set of exogenous variables (second stage). I want to calculate the effect of an endogenous ...
user21541837's user avatar
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Two questions about Interaction-terms in IV-regressions (2SLS) in R

I am doing a 2SLS-model in R with panel data (n=800), where I want to include an interaction-term as Instrumental-Variable in the first-stage model. My first question is: Does that even make sense? ...
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ECM long-run elasticity with one I(2) variable

I am estimating a 2SLS using a time series simultaneous equation ECM. The purpose is to estimate the price elasticity of electricity demand. Assume that both price and demand are I(1) variables, ...
KjetilH's user avatar
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Manually calculate robust standard errors of 2SLS regression

I used the "systemfit" function in R to estimate a 2SLS model as it allows to specify the first and second stage separately which is important for my estimation. I need robust standard ...
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Should I take logarithm of weights in WLS regressions

I am new here. I have a question regarding the anlaytical weights used in ivreghdfe or reghdfe regressions. People usually take aweights in STATA, my question is how we deal with the weight if the ...
anniejerry's user avatar
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What's the difference between exogenous and endogenous identifiers?

What's the difference? Exogenous vs. Endogenous identifiers.
Dr. T's user avatar
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Are standard errors from a second stage with OLS always underestimated? [duplicate]

I use Stata. I build on Standard errors of a two stage least squares regression, Stata to compute manually the standard errors for my model: I cannot use standard packages (ivreg2 etc.) as the second ...
axel365's user avatar
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What is the 2SLS bias with a zero first stage in instrument analysis

I am trying to understand the impact in the IV estimate when zero coefficient is obtained in the first stage.
Chris's user avatar
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Can you use two stage least squares (instruments) on an endogenous categorical variable (Likert scale)?

I have an endogenous categorical variable (exlanatory variable) measured on a Likert scale (from 1-4) and I would like to instrument it via 2sls. I am wondering if this is a theoretically correct ...
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132 views

Is my instrumental variable too noisy?

I have an instrument, that I want to use with IV 2SLS, to predict my endogenous variable. The scatter plot of my instrument against my endogenous variable looks like this. Using Stata's binscatter, I ...
Xavi's user avatar
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2sls second stage statistically insignificant

i conducted a two stage least square regression. The coefficients of my first stage are statistically significant, but my second stage is not. How can i interpretate this? My F-Statistic of the second ...
Lola's user avatar
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Prediction of the 1st stage in 2SLS not important?

My question was sparked by the discussion Why is the functional form of the 1st stage in 2SLS not important? I understand that in the first-stage we aim to predict our endogenous variable ($\hat{x}$), ...
An economist's user avatar
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443 views

Why not simply use your instrumental variable as your independent variable?

I'm a little confused as to why we need to go through an entire two-stage regression process to capture the effect of our instrumental variable on our independent variable, and then only use this ...
fruitless fruit juice's user avatar
3 votes
0 answers
82 views

Why is ignoring prediction error not a concern in instrumental variables?

In his book, Statistical Rethinking (2nd edition, p. 137), Richard McElreath states that including parameters with unobserved values, such as residuals, and treating them as if they were perfectly ...
Erik Eliassen's user avatar
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Interpretation of bias with an endogenous variable

I am running an analysis of impacts of immigration on natives' votes to anti-immigration parties, across municipalities. The concern in this type of analysis is that location decisions of immigrants ...
Xavi's user avatar
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278 views

Instrumental Variables: satisfying exclusion criterion with Covariates

I have encountered a situation wherein I am trying to ascertain the causal effect of X on Y through an IV approach in a cross-country panel study, but the exclusion restriction is not entirely valid. ...
Yoda's user avatar
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3 votes
1 answer
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Identifiability of multivariate instrumental variable model

I'm interested in estimating the effects of $X_1$ and $X_2$ on $Y$ in the directed acyclic graph below. $U_1$ and $U_2$ are unobserved confounders. Based on Definition 7.4.1 on p. 248 of Causality ...
bilgelm's user avatar
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1 answer
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Measuring the effect of a variable that moves through another variable

Model Let's say that I have a regression as follows: $$ Income_{ti} = B_0 + B_1Education_{ti} + B_2ControlA_{ti} + B_3ControlB_{ti} + u $$ Education is endogenous, and is in turn determined by: $$ ...
Tom's user avatar
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If I have two endogenous variables for which I each have an instrument, do I absolutely have to use both of them in both first stages?

I am estimating a model with two survey questions, which I expect to be endogenous by 2SLS: $$ Outcome_i = B_0 + B_1SurveyQuestionA_i + B_2SurveyQuestionB_i + B_3Control + u$$ I have an instrumental ...
Tom's user avatar
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2 answers
518 views

Size of Complier Group (Instrumental Variables) - Mostly Harmless vs. Abadie Kappa

Focusing solely on the case with a binary endogenous explanatory variable $D$ and binary instrument $Z$ and control variables $X$, Angrist & Pischke 2009 ("Mostly Harmless Econometrics") ...
jrm's user avatar
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Log Likelihood for Two Stage Least Squares (for AIC or BIC)

I'm looking to use a number of information criteria (BIC, AIC, etc.) for Two Stage Least Squares. Of course all information criteria need a log likelihood - and I'm also aware that for a Log-...
Moritz Schwarz's user avatar
1 vote
0 answers
87 views

How to estimate 2SLS using ratio of covariance in a presence of a vector of exogenous variables?

I am trying to estimate 2SLS using some simulated data, just to understand the theory behind it. First, I did it with just one endogenous variable ($X$) and one instrument ($Z$). Supposing the classic ...
Oalvinegro's user avatar
1 vote
0 answers
711 views

Control Function (CF) / Two Stage Residual Inclusion (2SRI) - with an ordinal EEV - in Stata

I am mostly an R user. But since I have not found a way yet to reproduce generalised residuals in R (link), I am using Stata for ...
Tom's user avatar
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Generalised Residuals - Estimated value of the density at that point for observation $j$ $i$?

I am trying to write R code for the generalised residuals as described in Vella (1993) and also mentioned by Wooldridge (2014). Wooldridge suggests to use these ...
Tom's user avatar
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How to do a Control Function (CF) / Two Stage Residual Inclusion (2SRI) with an ordinal dependent variable in the first stage and a glm in the second

I am trying to use a Control Function (CF) / Two Stage Residual Inclusion (2SRI) approach, because the modeled relationship that I am trying to estimate is non-linear (my dependent variable has a ...
Tom's user avatar
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1 vote
1 answer
468 views

Why including extra instrument variables in 2SLS changes my regression coefficients?

For example, when I include $A_i$ as my first instrument variable, I got the causal parameter estimate $=0.0592$ and if I included one more IV, $B_i$, my causal parameter estimate changes to $0.0505$. ...
Edi's user avatar
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380 views

2SLS approach using lagged dependent variable as an instrument

I was wondering if the lagged dependent variable can be a valid instrument or not. In my data, policy intervention (x) is made depending on the outcome (y) in the past. (not depending on the effect (b)...
Yendao Su's user avatar
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39 views

What is 2SLS estimator with three instruments?

Given the following model, $$y_i = a + bx_i +e_i$$ It's known that $Cov(e, x ) \neq 0$, so we are going to use 2SLS method. We have three variables $v_1, v_2, v_3$. What is the formula for the slope $\...
ElonMuskofBadIdeas's user avatar
1 vote
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430 views

How to decide whether to use robust errors in 2sls estimation

For my data, I have run both the OLS and IV regression to investigate the effects of health on salary. The BP test showed Heteroskedasticity for the OLS error terms so I decided to run the OLS ...
rainbow21's user avatar
1 vote
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293 views

What is the effect of an omitted variable in the first stage of an IV/2SLS

Background Let me start with the fact that I read, this post, this post and this post. These questions deal with omitting exogenous variables from the main equation in the first stage. My question is ...
Tom's user avatar
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2stage (instrumental variable) analysis: is reverse causality in the first stage a problem? [duplicate]

For my research I am looking into the relationship between an outcome (Y) and a predictor (X) as follows: $$Y = X + e$$ where $e$ is the error term. Because there might be reverse causality I am ...
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